How to render a sky in game engine?
Add a 'Scene' actuator in 'Add Background Scene' mode and add a Scene to the background of the current scene. You have lots of options when doing this.

See the example file, where I mixed two scenes and (using Python) I copied the rotation of the 'game' scene camera to the 'skybox' scene camera. Try to read the script, see the logic bricks, explore the scenes and you will understand how this method is powerful, allowing you to make a dynamic skybox in a scene and simply adding it to the main game scene.

http://pasteall.org/blend/index.php?id=48431

Alternatively, make a skybox object and parent to a single vertex of your game character. The skybox will follow your character location, but not the rotation, which is good for a sky.